• Journal of the Korea Concrete Institute
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• v.11 no.5
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• pp.79-88
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• 1999

The purpose of this paper is to develop a mathematical expression for computing crack angles based on reinforcement volumes in the longitudinal and transverse directions, member end-fixity and length-to-width aspect ratio. For this a reinforced concrete beam-column element is assumed to possess a series of potential crack planes represented by a number of differential truss elements. Depending on the boundary condition, a constant angle truss or a variable angle truss is employed to model the cracked structural concrete member. The truss models are then analyzed using the virtual work method of analysis to relate forces and deformations. Rigorous and simplified solution schemes are presented. An equation to estimate the theoretical crack angle is derived by considering the energy minimization on the virtual work done over both the shear and flexural components the energy minimization on the virtual work done over both the shear and flexural components of truss models. The crack angle in this study is defined as the steepest one among fan-shaped angles measured from the longitudinal axis of the member to the diagonal crack. The theoretical crack angle predictions are validated against experimentally observed crack angle reported by previous researchers in the literature. Good agreement between theory and experiment is obtained.

• Journal of the Korea Concrete Institute
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• v.12 no.6
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• pp.57-66
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• 2000

The truss analogy for the analysis of beam-columns subjected of shear and flexure is limited by the contribution of transverse and longitudinal steel and diagonal concrete compression struts. However, it should be noted that even though the behavior of reinforced concrete beam-columns after cracking can be modeled with the truss analogy, they are not perfect trusses but still structural elements with a measure of continuity provided by a diagonal tension field. The mere notion of compression field denotes that there should be some tension field coexisting perpendicularly to it. The compression field is assumed to form parallel to the crack plane that forms under combined flexure and shear. Therefore, the concrete tension field may be defined as a mechanism existing across the crack and resisting crack opening. In this paper, the effect of concrete tensile properties on the shear strength and stiffness of reinforced concrete beam-columns is discussed using the Gauss two-point truss model. The theoretical predictions are validated against the experimental observations. Although the agreement is not perfect, the comparison shows the correct trend in degradation as the inelasticity increases.

• Journal of the Korea Concrete Institute
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• v.12 no.5
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• pp.81-92
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• 2000

A fixed angle softened truss model has been developed in order to predict both shear strength and deformation of reinforced concrete members. The model takes into account the contribution of concrete by accuming the angle of cracks in the postcracking concrete that coincides with the reinforced concrete principal compressive angle determined by the applied stresses. Therefore, this model is capable of predicting the contribution of concrete from the govering equilibrium and compatibility equations including the shear stress and strain developed along concrete diagonal crack. However, the model has a limiting range to be applicable for reinforced concrete members. This research proposes a new algorthm of fixed angle softened truss model capable of removing the limitation of applicability. The proposed algorithm adopts a new conception of constitutive laws. The average normal stresses of concrete in the x- y- directions can be calculated by transforming the principal stresses of concrete. The proposed algorthm is verified by comparing to the test results.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.11a
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• pp.873-878
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• 2001

This Paper Presents a new model, called the “shear-friction truss model,” for slender reinforced concrete beams to derive a clear and simple equation for their ultimate shear strength. In this model, a portion of the shear strength is provided by shear reinforcement as in the traditional truss model, and the remainder by the shear-friction mechanism. Friction resistance is derived considering both geometrical configuration of the rough crack surface and material Properties. The inclined angle of diagonal strut in the traditional truss model is modified to satisfy the state of balanced failure, when both stirrups and longitudinal reinforcement yield simultaneously. The vertical component of friction resistance is added to the modified truss model to form the shear-friction truss model. Test results from published literatures are used to find the effective coefficient of concrete strength in resisting shear on inclined crack surfaces.

• Journal of the Korea institute for structural maintenance and inspection
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• v.24 no.2
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• pp.60-67
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• 2020

Recently, many studies have been conducted on the structural behavior of HPFRCC, but most of the studies focused on the flexural behavior while studies on the shear behavior are limited. In this study, a model has been developed to reasonably predict the shear strength of a HPFRCC beam without stirrups. To develop the model, a HPFRCC beam was simply idealized with upper & lower chords resisting bending moment and a web shear element resisting shear forces. Then, taking into the account of the tensile behavior of HPFRCC, the main diagonal compressive strut angle and shear stress of the web shear element were evaluated on shear failure. Then, the shear strength of the HPFRCC beam could be evaluated. For the verification of the proposed model, the predictions by the proposed model were compared with the test results of 48 HPFRCC beams exhibiting shear failure. The results showed that the proposed model reasonably predicted the actual shear strength with an average of 1.045 and CoV of 0.125. This study are expected to be useful for related researches and design of members or structures to which HPFRCC is applied.

• Earthquakes and Structures
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• v.7 no.5
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• pp.647-665
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• 2014

Squat reinforced concrete walls require enough shear strength in order to promote flexural yielding, which creates the need for designers of an accurate method for strength prediction. In many cases, especially for existing buildings, strength estimates might be insufficient when more accurate analyses are needed, such as pushover analysis. In this case, estimates of load versus displacement are required for building modeling. A model is developed that predicts the shear load versus shear deformation of squat reinforced concrete walls by means of a panel formulation. In order to provide a simple, design-oriented tool, the formulation considers the wall as a single element, which presents an average strain and stress field for the entire wall. Simple material constitutive laws for concrete and steel are used. The developed models can be divided into two categories: (i) rotating-angle and (ii) fixed-angle models. In the first case, the principal stress/strain direction rotates for each drift increment. This situation is addressed by prescribing the average normal strain of the panel. The formation of a crack, which can be interpreted as a fixed principal strain direction is imposed on the second formulation via calibration of the principal stress/strain direction obtained from the rotating-angle model at a cracking stage. Two alternatives are selected for the cracking point: fcr and 0.5fcr (post-peak). In terms of shear capacity, the model results are compared with an experimental database indicating that the fixed-angle models yield good results. The overall response (load-displacement) is also reasonable well predicted for specimens with diagonal compression failure.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.20 no.5
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• pp.569-576
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• 2019

PSC-Edge Rahmen Bridge makes low thickness and long span by introducing prestressed force to the edge girder and reducing positive moment. In the bridge, diagonal tension cracks occurred in the direction of $45^{\circ}$ to outer side of the girder after the temporary bent supported on the lower part of the upper slab and the secondary strand is tensioned on the girder. Researches on stress distribution and burst crack behavior of pre-stress anchorage has been conducted, it is difficult to analyze an obvious cause due to difference between actual shape and boundary condition. This study performed 3D frame analysis with additional boundary condition of temporary bent, the maximum compression stress occurred in the girder and there was a limit to identify the cause. It performed 3D Solid analysis with LUSAS 16.1 and the maximum principal tensile stress occurred at the boundary between the girder and the slab. As analyzing required reinforcement quantity at obtuse angle of the girder with the maximum principal tensile stress and directional cosine, reinforcement quantity was insufficient. Additional bridges have increased reinforcement quantity and extended area and crack was not occurred. It is expected that cracks on the girder during construction could be controlled by applying the proposed method to PSC-Edge Rahmen Bridge.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.2
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• pp.1-10
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• 1992

In this study, the 'Comb-structure' model which has been developed from truss analogy is modified in order to be applied to the shear analysis of partially prestressed concrete members. The proposed 'Comb-structure' model is modified so that the position, the slope of concrete compressive chord and the slope of concrete diagonal strut may change according to the magnitude of loads and prestress. For the proposed mechanical model, non-linear beam and truss elements are used. By modifying the 'Compression-Field' theory, the equation to determine the slope angle of concrete diagonal strut can be induced. The anaysis results by the proposed 'Comb-structure' model are compared with the experimental results and validity of model is examined. It shows that the the result of 'Comb-structure' analysis lies between that of the modified M$\ddot{o}$rsch theory and classical M$\ddot{o}$rsch theory, and close to the measured value after cracking. The deflection of the beam and the stress of stirrup show good agreement, so it can be concluded that the proposed 'Comb-structure' analysis model explains the shear behavior of partially prestressed concrte beams after crack initiation.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.11a
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• pp.879-884
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• 2001

The use of recycled-aggregate concrete is increasing faster than the development of appropriate design recommendations. In addition, recycled-aggregate and higher compressive strengths are two of the most desired characteristics to improve the use of concrete as a construction material. The paper reports limited experimental data on the shear capacity of high-strength recycled aggregate concrete beams. Ten beams were tested to determine their diagonal cracking and ultimate shear capacities. The variable in the test program were concrete strength(300, 500 and 700kgf/$cm^{2}$), and shear span/depth ratio (a/d : 2.0, 3.0 and 4.0). Test results indicate that the ACI Building code prediction of Eq.(11-3) and (11-5) for high-strength recycled aggregate concretes are unconservative for all beams (with concrete strength 300, 500 and 700kgf/$cm^{2}$, a/d ratios 2.0, 3.0 and 4.0). But Zsutty Equation for high-strength recycled aggregate concretes is conservative for all beams. The results of the experimental investigation on the cracking patterns for beams show that the angle that the critical inclined crack makes with the horizontal axis decreases with increasing a/d.

• Journal of the Korea Concrete Institute
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• v.22 no.5
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• pp.703-710
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• 2010

Reinforced concrete beams of existing structure often encounter insufficient shear problems for various reasons. Application of steel plates is one of widely used methods for shear strengthening of reinforced concrete beams that are insufficient of shear capacity. This study presents test results on strengthening shear deficient RC beams by external bonding of vertical and diagonal slit type steel plates with anchor bolt. Test parameters are width, interval, angle and length of slits with anchor bolt. The purpose was to evaluate the failure modes and shear capacities for RC beams strengthened by various slit type steel plates with anchor bolt. The results showed that the slit type steel plate specimens strengthened by adhesive bonding and bolting failed in shear fracture modes at maximum load. Flexural crack first occurred on the tension face of beam and then inclined cracks occurred on the shear span. Finally, slit type steel plates strengthened by adhesive bonding and fastening bolts managed to delay abrupt debonding and didn't detach fully from main body of RC beam.